Vehicle transport arrangements of this kind are known from SE-B-459 110, SE-B-463 219 and SE-B-465 585 and function relatively well. However, it has been found difficult to satisfactorily resolve the problem of moving the vehicle supporting carriages relative to the transfer carriage which carries these carriages as they are transported from and to a respective drive-in module and drive-out module to and from a location opposite a parking space and into and out of a parking space respectively. One cause which contributes to these difficulties is that the distance through which the vehicle, and therewith the vehicle-carrying carriages, shall be moved coincides essentially with the extension of the transfer carriage in the direction of vehicle movement and is therewith long in relation to the space at the disposal of the vehicle moving devices. The transport arrangement described in SE-B-463 219 uses linear gearing which includes two rods that can be moved relative to one another and which are driven by a relatively complicated chain mechanism, said gearing taking-up a relatively small amount of space when the rods are retracted.